Hydraulic Reservoir System The system shown in the figure represents two large h

Question

Hydraulic Reservoir System

The system shown in the figure represents two large hydraulic reservoirs connected by a long uniform line. Using the symbols and notation defined in the figure, the equations of motion for this system can be shown to be:

Note that  is the fluid density, Ai are the cross-sectional areas, hi(t) are the heights above the points i=1 and 2, and zi are constant reference heights of the points i above a datum. Note that the wi(t) represent mass flow rates, and Ci are constants of appropriate units.

*  Describe an engineering application that the project topic will be used to model. For your system, define variables (i.e. inputs, outputs, states), give assumptions (e.g. linearity of elements, rigidity of components) and derive the equations of motion to confirm those given.

* A non-linearity is included in one or more components of the system. Systematically apply linearization to this nonlinear system to derive linearized equations. 

Explanation / Answer

1 + 2 + 3 + 4 = 10

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